Piece of Cake
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
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Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
How would you cut a rectangular cake o two equal pieces when a rectangular piece has already been cut out of it? The cut piece can be of any size and orientation. You are only allowed to make one straight cut.
Solution:
There are two possible solutions to this problem. People often overlook the easier solution to this problem. Let’s start with the easiest solution. If you make one straight horizontal cut along the height of the cake the resulting slices are of equal sizes. But this solution may not work so well on a cake with icing. So let’s rethink. In general when a straight cut is made at any angle through the center of a rectangle the resulting pieces are always of equal area. So let’s consider our situation. What if we make a straight cut such that it passes through the center of both the rectangles? Since the cut halves both the rectangles the resulting two pieces are guaranteed to have equal area. Each piece has an area equal to half the original cake minus half the area of the missing rectangular piece. This results in two pieces of equal size asing the cake’s height is same at all pos
How would you cut a rectangular cake o two equal pieces when a rectangular piece has already been cut out of it? The cut piece can be of any size and orientation. You are only allowed to make one straight cut.
Solution:
There are two possible solutions to this problem. People often overlook the easier solution to this problem. Let’s start with the easiest solution. If you make one straight horizontal cut along the height of the cake the resulting slices are of equal sizes. But this solution may not work so well on a cake with icing. So let’s rethink. In general when a straight cut is made at any angle through the center of a rectangle the resulting pieces are always of equal area. So let’s consider our situation. What if we make a straight cut such that it passes through the center of both the rectangles? Since the cut halves both the rectangles the resulting two pieces are guaranteed to have equal area. Each piece has an area equal to half the original cake minus half the area of the missing rectangular piece. This results in two pieces of equal size asing the cake’s height is same at all pos
Meta Information
Exercise:
How would you cut a rectangular cake o two equal pieces when a rectangular piece has already been cut out of it? The cut piece can be of any size and orientation. You are only allowed to make one straight cut.
Solution:
There are two possible solutions to this problem. People often overlook the easier solution to this problem. Let’s start with the easiest solution. If you make one straight horizontal cut along the height of the cake the resulting slices are of equal sizes. But this solution may not work so well on a cake with icing. So let’s rethink. In general when a straight cut is made at any angle through the center of a rectangle the resulting pieces are always of equal area. So let’s consider our situation. What if we make a straight cut such that it passes through the center of both the rectangles? Since the cut halves both the rectangles the resulting two pieces are guaranteed to have equal area. Each piece has an area equal to half the original cake minus half the area of the missing rectangular piece. This results in two pieces of equal size asing the cake’s height is same at all pos
How would you cut a rectangular cake o two equal pieces when a rectangular piece has already been cut out of it? The cut piece can be of any size and orientation. You are only allowed to make one straight cut.
Solution:
There are two possible solutions to this problem. People often overlook the easier solution to this problem. Let’s start with the easiest solution. If you make one straight horizontal cut along the height of the cake the resulting slices are of equal sizes. But this solution may not work so well on a cake with icing. So let’s rethink. In general when a straight cut is made at any angle through the center of a rectangle the resulting pieces are always of equal area. So let’s consider our situation. What if we make a straight cut such that it passes through the center of both the rectangles? Since the cut halves both the rectangles the resulting two pieces are guaranteed to have equal area. Each piece has an area equal to half the original cake minus half the area of the missing rectangular piece. This results in two pieces of equal size asing the cake’s height is same at all pos
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